Cell facilitation promotes growth and survival under drug pressure in breast cancer

The interplay of positive and negative interactions between drug-sensitive and resistant cells influences the effectiveness of treatment in heterogeneous cancer cell populations. Here, we study interactions between estrogen receptor-positive breast cancer cell lineages that are sensitive and resistant to ribociclib-induced cyclin-dependent kinase 4 and 6 (CDK4/6) inhibition. In mono- and coculture, we find that sensitive cells grow and compete more effectively in the absence of treatment. During treatment with ribociclib, sensitive cells survive and proliferate better when grown together with resistant cells than when grown in monoculture, termed facilitation in ecology. Molecular, protein, and genomic analyses show that resistant cells increase metabolism and production of estradiol, a highly active estrogen metabolite, and increase estrogen signaling in sensitive cells to promote facilitation in coculture. Adding estradiol in monoculture provides sensitive cells with increased resistance to therapy and cancels facilitation in coculture. Under partial inhibition of estrogen signaling through low-dose endocrine therapy, estradiol supplied by resistant cells facilitates sensitive cell growth. However, a more complete blockade of estrogen signaling, through higher-dose endocrine therapy, diminished the facilitative growth of sensitive cells. Mathematical modeling quantifies the strength of competition and facilitation during CDK4/6 inhibition and predicts that blocking facilitation has the potential to control both resistant and sensitive cancer cell populations and inhibit the emergence of a refractory population during cell cycle therapy.

. Imaging was performed using Cytation 5 imager (Biotek Instruments) recording signal intensity from brightfield, YFP (for Venus fluorescence) CFP 450/440 (for Cerulean fluorescence) and Texas Red (for mCherry fluorescence) channels. Raw data processing and image analysis were performed using Gen5 3.05 and 3.10 software (Biotek Instruments). Briefly, the stitching of 2 × 2 montage images and Z-projection of 6 layers using focus stacking was performed on raw images followed by spheroid area analysis. To quantify growth under these conditions, we measured fluorescence intensity and growth of spheroid area over the total time of the experiment. For cell count calculations, a standard curve was created by measuring spheroid and fluorescent intensity 24 hours after plating at different cell numbers. To predict cell numbers of other samples, a polynomial equation was fitted to the standard curve data using GraphPad Prism 7.02 software (second order polynomial -quadratic -curve fit used). Whole spheroid area and fluorescence intensity measurements of each population were integrated into the fitted equation, and cell counts for each population were produced from fluorescence intensities relative to spheroid size. All coculture experiments were performed in triplicates.

Multiplex cytokine analysis
Media samples taken at day 21 from 3D spheroid experiments, treated with or without ribociclib, (experimental setup previously described in results and methods -Mono-and coculture 3D spheroid experiments) and plated in different compositions (100% sensitive, 50% sensitive -50% resistant, and 100% resistant) were spun down at 300g and frozen at -80 o C. Samples were then prepared by the Analytical Pharmacology Core of City of Hope National Medical Center for multiplex cytokine analysis. Samples were analyzed for 5 cytokines (EGF, FGF2, FGF21, FGF23, and TGFα) using the "ProcartaPlex Multiplex Immunoassay Kit" (Invitrogen, Camarillo, CA) per manufacturer's protocol. In addition, TGFβ-1, -2, and -3 were measured using the "Magnetic Luminex Performance Assay Kit" (R&D Systems, Minneapolis MN) also according to manufacturer's instructions. For analysis of TGFβ, the latent proteins required activation to their immunoreactive state prior to detection. Activation was accomplished by adding 20 µl of 1N HCl to 100 µl of sample followed by incubation for 10 minutes at room temperature. Samples were then neutralized by the addition of 20 µl of 1.2N NaOH/0.5M HEPES prior to dilution and loading on to the plate. Briefly, multiplex bead solutions were vortexed for 30 s and 50 µl was added to each well and then washed twice with wash buffer. Next, 50 µl of sample (cell culture supernatant) was loaded in duplicate into Greiner flat-bottom 96 well microplates. Cytokines standards were reconstituted with unconditioned cell culture medium and serial dilutions were prepared. Plates were then incubated on a plate shaker at 500 rpm in the dark at room temperature for 2 hours. The plate was then applied to a magnetic device designed to accommodate a microplate and all wells were washed two times with 200 µl of wash buffer. Biotinylated detection antibody mix (25 µl) was added to each well and the plate was incubated on the plate shaker for another hour. After washing two times with 200 µl of wash buffer, streptavidin-phycoerythrin (50 µl) was added to each well followed by incubation on a plate shaker for 30 minutes. After two more washes, the contents of each well were resuspended in 120 µl reading buffer and shaken for 5 min. Finally, the plate was transferred to the Flexmap 3D Luminex system (Luminex corp.) for analysis, cytokine concentrations were calculated using Bio-Plex Manager 6.2 software with a five parameter curve-fitting algorithm applied for standard curve calculations for duplicate samples.

Ribociclib concentration measurements with high performance liquid chromatographymass spectrometry (HPLC/MS)
Spheroid experiments were initiated as earlier described (Mono-and coculture spheroid experiments) with some modifications. CAMA-1 sensitive and resistant cells were plated at different cell numbers (2,000; 10,000; 40,000) and in different compositions (100% sensitive, 50% sensitive -50% resistant, and 100% resistant). After 24 hours, ribociclib treatment (400nM) was applied for 4 days. Following the 4-day treatment, media from cell samples were spun down at 300g and frozen at -80 o C. Samples were then prepared by the Analytical Pharmacology Core of City of Hope National Medical Center for HPLC/MS. Media without cells (+/-drug) were also subjected to HPLC/MS measurements. Acetonitrile (ACN) and methanol were of HPLC-grade and purchased from Fisher Scientific (Fair Lawn, NJ, USA). Ammonium acetate was purchased from Mallinckrodt (Kentucky, USA). Ribociclib and abemaciclib (internal standard) were provided by Selleck Chemicals. Deionized water was prepared using the Millipore Milli-Q system (Milford, MA, USA). Abemaciclib measurements were optimized to provide negative control.
Samples were prepared for analysis by mixing 30 µl of media with 10 µl 50% methanol in water in a 0.5 ml low retention micro-centrifuge tube. To this tube, 10 µl of 6 µM abemaciclib in 50% methanol and 180 µl of ice cold methanol were added. The tube was then vortex mixed for 3 minutes and centrifuged for 5 minutes at highest speed and 4°C. Following centrifugation, 20 µl of the supernatant was mixed with 180 µl of 50% methanol in 50% 10mM ammonium acetate. The final solution was then transferred to an autosampler vial and 2 µl was injected on column.
LC-MS/MS analysis was performed using a Waters Acquity UPLC system (Milford, MA, USA) interfaced with a Waters Quattro Premier XE mass spectrometer. HPLC separation was achieved using a Gemini NX C18, 100 x 2.1mm column (Phenomenex, Torrance, CA, USA) proceeded by a Phenomenex Gemini NX C18 guard column (Torrance, CA, USA). The column temperature was maintained at 40°C. Isocratic elution was performed using a mobile phase of 15% 6 mM ammonium acetate in ACN at a flow rate of 0.3 ml/min. Under optimized chromatographic conditions, the retention times were 1.2 minutes and 1.89 minutes for ribociclib and abemaciclib, respectively. The total run time was 4 minutes.
The electrospray ionization source of the mass spectrometer was operated in positive ion mode with a cone gas flow of 25 L/hr and a desolvation gas flow of 750 L/hr. Capillary voltages were 0.4 kV for both ribociclib and abemaciclib, and the cone voltages were optimized at 45 V for ribociclib and 28 V for abemaciclib, respectively. The collision voltages were set to 32 V for ribociclib and 28 V for abemaciclib. The source temperature was 125°C and the desolvation temperature was 470°C. Multiple reaction monitoring (MRM) was used for quantitation and the optimal precursor  product ion combinations were determined to be 435.34  321.9 m/z and 507.32  392.92 m/z for ribociclib and abemaciclib, respectively. MassLynx version 4.1 software was used for data acquisition and processing.

Total exosome isolation experiment
Spheroid experiments were initiated as earlier described (Mono-and coculture spheroid experiments) with some modifications. CAMA-1 sensitive and resistant cells were plated at 2,000 cells per well and in different compositions (100% sensitive and 100% resistant). These spheroids were treated with or without 400nM ribociclib and designated as donor wells. On every 3rd and 6th day of the week media was changed on the donor wells and exosomes were isolated from the old media using Total Exosome Isolation Reagent (from cell culture media, Thermo Fisher, Cat. No.: 4478359) according to the manufacturer's protocol. Briefly, cell culture media was centrifuged at 2000Xg for 30 minutes to remove cells and debris, and 200 uL supernatant was mixed with 100 uL Total Exosome Isolation Reagent and incubated on 4C overnight. Following this incubation, samples were centrifuged at 10,000Xg for 60 minutes at 4C and exosomes were resuspended in PBS. Exosomes (either from untreated or ribociclib treated, 100% sensitive or 100% resistant donor wells) were isolated from this procedure and added to the media of other 100% sensitive spheroids, designated as acceptor wells, during media change on every 4th and 7th day of the week. During this media change, 75% of media was untreated or 400nM ribociclib treated complete media with the remaining 25% contribution of isolated exosomes originating from donor wells. Imaging of each well was performed on every 4th and 7th day of the week as earlier described in methods using the Cytation 5 imaging system. Analysis was completed as previously described in methods.
Differentially expressed genes between mono-culture and sensitive mono-culture treated with ribociclib To identify genes that are upregulated in resistant cells in monoculture, we used the 'FindMarkers' function from the Seurat package (version 4.3.0) with sensitive cells in monoculture as baseline. The Wilcoxon Rank Sum method was used to identify statistically significant genes. Genes were only considered for analysis if expression was detected in a minimum of 25% of cells. To be considered statistically significant, an average log-fold change of 0.5 and adjusted p-value of 0.05 were used as thresholds. Positive fold-change values represented genes enriched in resistant cells while negative fold-change values represented genes enriched in sensitive cells.

Description of FACT mechanistic model comparisons
Using formal model comparison, we compared the accuracy of our facilitation model's predictions of spheroid growth against predictions of alternative models describing direct competition for resources (Competition alone model) or phenotypic plasticity in which cells transition from a naive to a resistant state either in response to drug induction (Plasticity DI) or via random switching (Plasticity RS). Here we outline the set of differential equation models used to describe alternative hypotheses of mechanisms that govern the growth dynamics of monocultures and cocultures of resistant and sensitive cells (CAMA-1) grown under different doses of the cell cycle inhibitor ribociclib. Bayesian inference was used to fit each model to the growth trajectories of mono-and co-cultures of sensitive and resistant cells across 8 doses of ribociclib. We then present the model comparison results showing which hypotheses about the mechanisms of cell-cell interactions were supported by the data.
Defining alternative models describing hypothesized mechanisms governing spheroid growth dynamics

Competition alone
Populations of sensitive (S) and resistant (R) cells compete for resources to proliferate. The abundance of cell type ( ∈ { , }) within a spheroid ( ) depends on the balance of cell proliferation and death. Sensitive and resistant cells each divide at a baseline rate ( ) that is reduced by cell cycle inhibition (ribociclib; ). The susceptibility of each cell type to cell cycle inhibition depends on its parameter. Proliferation is also reduced through competition, with each cell type having a competitive effect equal to 1/ . Finally cell death occurs at rate . This yields the following competition model: Plasticity (DI): Drug induced phenotype switching Treatment may stimulate modified gene expression, inducing cells to transition to a more resistant state, perhaps through epigenetic reprogramming. We describe both the innately resistant and sensitive cells as transitioning from a naive state ( ) to an induced resistant state ( ). This transition rate ( ) is proportional to drug concentration. As in the competition alone model (above), proliferation depends on the ribociclib concentration and the abundance and competitiveness of naïve and induced cells of each lineage (resistant vs sensitive). Baseline proliferation and ribociclib susceptibility are allowed to differ between innately resistant and sensitive cells ( and , with ∈ { , ) and for each cell type when in a state of induced resistance ( ̃ and , with ∈ { , ) ). Cell death occurs at differing rates in induced and un-induced cells. This yields the following drug induced phenotype switching model:

Plasticity (RS): Random phenotype switching
Resistance related changes in gene expression might occur independent of treatment, for example depending on the cell cycle state that the cell happened to be in at the onset of treatment. We describe the resistant and sensitive lineages as transitioning from a naive state ( ) to an induced resistant state ( ) at a rate that is independent of treatment ( ). Cell proliferation and death is the same as in the drug induced phenotype switching model. This yields the following random phenotype switching model:

Facilitation Symmetric (1D): Allee effect model of facilitation
We first describe facilitation between resistant and sensitive cells in which cells of both lineages contribute equally to the facilitation effect on a per cell basis (symmetric facilitation effects). We describe the production of a facilitation factor that is produced at rate in both cell types. The beneficial effect of the facilitation factor saturates at high concentrations, with the asymptotic benefit at high densities equaling 1/ . This facilitation effect increases proliferation. The functional form of competition, the drug impact and cell death are the same as in the competition model. This yields the following Allee effect model of symmetric facilitation:

Facilitation (1D): Asymmetric contribution to facilitation
The production and decay of a facilitation factor ( ) can be modelled explicitly to account for the differences in production by sensitive and resistant cells. Cells of each cell type produce the facilitation factor at rate and it decays at rate . The concentration of the facilitation factor determines the proliferation promotion benefit. As with the symmetric facilitation model, this benefit saturates at high concentrations, with an asymptotic benefit of 1/ . The functional form of competition, the drug impact and the cell death are again the same as in the basic competition model. With in quasi steady state and symmetric contributions of cell types to facilitation, this reduces to the Allee effect model of facilitation.

Facilitation (2D): Asymmetric contribution to facilitation & cell quiescence
To describe the mechanism of action of ribociclib treatment more mechanistically, we use the stage-structured modeling approach to create a minimal population level model to predict the effects of cell cycle inhibition treatment (1).
With this approach, cells transition from a proliferative ( ), to a quiescent ( ) state. Proliferative cells enter the G1/S phase cell cycle checkpoint at a baseline rate ( ), which is reduced by resource competition ( ( , )) and increased by estradiol availability ( ). Resource competition between cells is described by ( , ) = 1 − ∑ , where competitive ability of each cell type ( ) is determined by the carrying capacity parameter .
As in the 1D facilitation model, the extracellular concentration of the facilitation factor ( ) depends on its differing net production by sensitive and resistant cells ( ) and its decay ( ). Additionally, we describe the intracellular concentration of facilitation factors, which depends on the balance of production by the cell and the influx into the cell against diffusion out of the cell and binding. This leads to the intracellular steady state concentration of cell type of: = .
Cell entry into the G1/S phase checkpoint increases with the intracellular level of estradiol ( ) and increased receptor binding ( ), saturating at high concentrations when uptake and binding becomes rate limited ( ). We describe this as: = (1 + ) ( , ). Cells at the G1/S phase checkpoint undertake a decision to divide or enter a quiescent state, based on the balance of key regulatory cell cycle promoters and inhibitors. Cell cycle inhibition using ribociclib ( ) inactivates key promoters of the G1/S checkpoint transition, blocking cell cycle progression and increasing the probability of quiescence above the baseline ( ) according to ( ) = .
Here the half-saturation constant ( ) can differ between resistant and sensitive cells to quantify drug susceptibility. Cells enter the G1/S phase checkpoint (at per cell rate G ) and undertake a binary decision to either i) quiesce at a rate G q (x) (which increases with ribociclib dose) or ii) divide if they do not quiesce at rate G 1 − q (x) . Following quiescence, cell death occurs at rate .
Together these components capturing competition, facilitation, cell cycle progression and arrest yield the population model:

Facilitation (3D): Asymmetric contribution to facilitation & cell quiescence and senescence
Finally, we extend the stage structured model to describe the transition from proliferative ( ), to quiescent ( ) and senescent ( ) cell states.
Proliferative cells enter the G1/S phase cell cycle checkpoint at a baseline rate ( ), which is reduced by resource competition ( ( , , )) and increased by estradiol availability ( ).
Resource competition between all three cell states extends to: ( , , ) = 1 − ∑ , where competitive ability of each cell type ( ) is determined by the carrying capacity parameter . As above, cell entry into the G1/S phase checkpoint increases with the intracellular level of estradiol ( ) and increased binding ( ), saturating at high concentrations when uptake and binding becomes rate limited ( ), which we describe as: . Cells in the G1/S phase checkpoint either divide or enter a quiescent state, following the same mechanism as described in the 2D facilitation model. However, following quiescence, cells transition into the final senescent state at rate before cell death occurs at rate . Although structurally and mechanistically similar, this model produces additional delays in the drug effects on population abundances. This full model and its derivation is described in more detail in the methods section but follows: Bayesian inference report: Fitting the Estradiol mediated facilitation model to spheroid growth trajectories Here we provide details of the inference workflow used to parameterize the Estradiol mediated facilitation model (reported in the main text; Facilitation (3D), as well as the comparison models defined above). Such models are necessarily nonlinear, to incorporate density and dose dependent interaction between cells, dynamical to describe growth trajectories over time and must account for the unmeasured state of the facilitation factor (a latent variable of the model). Posterior parameter distributions of the model (detailed in the methods) were estimated using Markov Chain Monte Carlo (MCMC) simulations. We used the STAN statistical programming language, to conduct efficient Bayesian inference though its implementation of gradient-based MCMC algorithms (Hamiltonian Monte Carlo). Stan was accessed via the "rstan" package (version 2.19.2) in R (2-3).

Priors
Under a given set of parameters, the probability density of observations was evaluated against prior beliefs and the log normally distributed likelihood model. The model parameters were all constrained to be non-negative and were given weak prior with wide distribution to reflect uncertainty. The parameters' description, prior and its rational are presented in Supplementary Table 1. Crucially, for each parameter that was allowed to vary between sensitive and resistant cells (indicated by parameter subscripts) the same prior distribution was applied for each cell type's parameter. This avoided biasing posterior inferences and meant that all differences in between sensitive and resistant cells were informed by the spheroid trajectory data that contribute to the model likelihood. Finally, estimation was performed on log transformed parameter values and a Bayesian shrinkage term (parameter~Normal(mean=prior expectation, sd= 2)) to restrain parameter values within biologically sensible ranges.

MCMC inference
For each model, we ran three independent MCMC chains, each with 4000 warm-up iterations followed by an inference phase of 1000 sampling iterations. This resulted in 3000 posterior samples for each parameter. Diagnostic checks were undertaken to ensure that inferences were reliable. We verified MCMC convergence by ensuring that the independent chains had convergent posterior probability and residual error early in the warmup phase (Supplementary Figure 12). To assess the performance of the MCMC inference algorithm, we examined the stability of posterior probability between the warmup and inference phase and verified a sufficient metropolis acceptance rate was obtained (Supplementary Figure  13). To verify that MCMC inference iterations represented independent samples of the posterior distribution of parameter space, we assessed the autocorrelation of MCMC states across different lags (Supplementary Figure 14). We identified a low correlation of MCMC states with previous iterations (autocorrelation > 0.5 by lag 5). The scale reduction factor of all parameters was assessed to be approximately 1. Finally, density plots were used to ensure parameter convergence of MCMC chains during the inference phase (Supplementary Figure). Posterior parameter estimates of each chain were overlapping and considerably narrower than the prior distributions, indicating that parameters were well informed by the data and that posteriors did not simply reflect the prior knowledge. In conclusion, the MCMC chains converged rapidly, were well mixed, stationary and not auto-correlated.

Assessment of posterior parameter estimates
For all biological processes in the model that varied between resistant and sensitive cells, we compared the parameter estimates and their uncertainty (Supplementary Figure 16). Our results show that as expected, sensitive cells had higher division rates ( ) and carrying capacity ( = 1/ ) (in the absence of treatment). However, sensitive cells also quiesce ( ), senesce ( ) and die ( ) more quickly in the absence of treatment. As expected, ribociclib treatment had a greater effect on sensitive cells, with their half maximum drug dose being lower ( ). Resistant cells produced the facilitation factor at a faster rate than sensitive cells ( ). Each biological parameter that varied between cell types (panel) had equal prior distributions for the belief of resistant and sensitive cell rates.
Results of models comparison showing which hypotheses were supported by the data    Supp. Figure 3.  Supp. Figure 4. Sensitive cells supplemented with isolated exosomes from conditioned media. Comparing growth of drug treated spheroids supplemented with exosomes derived from media taken from spheroids of either 100% sensitive (fluorescently labeled with green) or 100% resistant (fluorescently labeled with red) cells. a, Labeled cells were plated with the indicated composition of sensitive and resistant cells in 3D spheroids under no treatment or 400nM ribociclib treatment to produce conditioned media (donor wells). 25 % of total exosomes isolated from conditioned media of donor wells were added to acceptor wells (100% sensitive spheroids) with or without ribociclib treatment. Sample size is n=3 for each cell line/condition. b, Normalized spheroid area and cell count of sensitive cells (from "acceptor wells") supplemented with exosomes from untreated conditioned media generated from either 100% sensitive or 100% resistant cells. Sample size is n=3 for each cell line. Data plotted as mean with SD. c, Normalized spheroid area and cell count of sensitive cells (from "acceptor wells") supplemented with exosomes from treated conditioned media generated from either 100% sensitive or 100% resistant cells. Sample size is n=3 for each cell line. Data plotted as mean with SD. Source data provided in Source Data file.

Competitive Effects in MCF7 Cells
Supp. Figure   Supp. Figure 8. Facilitation in sensitive and resistant cells under single agent or combination treatment of ribociclib, estradiol, and fulvestrant. a, Method for calculating deviation from null model. Green arrow indicates the growth reduction due to treatment, purple arrow the growth reduction due to competition, and blue arrow the observed combined effect. Black curve indicates the expected growth if the two reductions operated independently, with the difference from observed showing facilitation. This notation is used in panels b-e, with the statistical framework as in Figure 1f. b, Sensitive cells received no facilitation from resistant cells in the presence of estradiol, growing less than predicted (n=3 for each treatment, the log ratio of observed cells to predicted cells decreased with time in a linear model, slope of the effect of day=-0.0125, SE=0.00341, p=0.0028). c, Sensitive cell growth in with ribociclib was reduced by a smaller amount with estradiol (n=3 for each treatment, the log ratio of observed cells to predicted cells increased with time in a linear model, slope of the effect of day=0.0949, SE=0.00473, p=3.7e-11, Supp. Figure 9. Modifications of facilitation and spheroid growth by other aromatase and endocrine inhibitors. CAMA-1 spheroids of different cell compositions (100% sensitive -green, 50% sensitive-50% resistant, 100% resistant -blue) cultured under different endocrine therapy treatments for 18 days; images taken on day 18. a, Spheroids cultured in untreated, 200nM ribociclib, 0.2uM letrozole, or combination 200nM ribociclib with 0.2uM letrozole treated medium b, Facilitation under letrozole and ribociclib treatments in terms of log growth relative to expected, averaged over all replicates, for CAMA-1 cells, n=3 for each treatment ; Letrozole in combination with ribociclib reduced but did not cancel facilitation (p=0.00063 for interaction of cell type with day using a linear model of the log of observed over expected cell number, effect size=0.0720, SE=0.0161). c, Spheroids cultured in untreated, 200nM ribociclib, 1000nM exemestane, or combination 200nM ribociclib with 1000nM exemestane treated medium d, Facilitation under exemestane and ribociclib treatments in terms of growth relative to expected averaged over all replicates for CAMA-1 cells, n=3 for each treatment; Exemestane in combination with ribociclib cancelled facilitation (p=0.6720 for interaction of cell type with day using a linear model of the log of observed over expected cell number). e, Spheroids cultured in untreated, 200nM ribociclib, 1uM tamoxifen, or combination 200nM ribociclib with 1uM tamoxifen treated medium f, Facilitation under tamoxifen and ribociclib treatments in terms of growth relative to expected averaged over all replicates for CAMA-1 cells, n=3 for each treatment; Tamoxifen in combination with ribociclib reversed facilitation (p=0.0070 for interaction of cell type with day using a linear model of the log of observed over expected cell number, effect size=-0.0285, standard error=0.0089). g, Spheroids cultured in untreated, 200nM ribociclib, 75nM raloxifene, or combination 200nM ribociclib with 75nM raloxifene treated medium h, Facilitation under raloxifene and ribociclib treatments in terms of growth relative to expected averaged over all replicates for CAMA-1cells, n=3 for each treatment; Raloxifene in combination with ribociclib reduced but did not cancel facilitation (p=4.0e-5 for interaction of cell type with day using a linear model of the log of observed over expected cell number, effect size=0.0306, standard error=0.0050). Source data provided in Source Data file and csv files beginning suppfig9.
Supp. Figure 11. Model comparison between alternative model hypotheses describing the mechanisms of cell-cell interactions impacting spheroid growth dynamics.
Comparison of the ability of facilitation models (green) to describe the resistant and sensitive CAMA1 spheroid growth data across drug doses, relative to models of phenotypic plasticity (red) or competition alone (blue). Low prediction error indicates that the model more accurately explains the spheroid growth data (n=504 spheroid measurements across 7 days, 8 doses and 2 cell types), whilst avoiding overfitting the data by penalizing the model likelihood based on model complexity (using WAIC: widely applicable information criterion). Error bars indicate the confidence interval around the models estimated goodness of fit.
Supplementary Figure 12. Bayesian inference converged. Estradiol mediated facilitation model inference performance during three independent MCMC chains. Bayesian inference converged early in the warmup period (shaded region; n=4000 Hamiltonian Monte Carlo iterations) of inference and the models posterior probability (left) and residual error (right) was stable throughout the inference phase (unshaded region; n=1000 Hamiltonian Monte Carlo iterations). MCMC samples from the warmup phase were discarded and the iterations from the inference phase were used to determine posterior parameter distributions.